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On the asymptotic analysis of surface-stress-driven thin-layer flow

In: Practical Asymptotics

Author

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  • Leonard W. Schwartz

    (Department of Mechanical Engineering The University of Delaware Newark)

Abstract

It has been demonstrated experimentally that thin liquid layers may be applied to a solid surface or substrate if a temperature gradient is applied which results in a surface tension gradient and surface traction. Two related problems are considered here by means of the long-wave or lubrication theory. In the first problem, an improved estimate of the applied liquid coating thickness for a liquid being drawn from a bath is found through asymptotic and numerical matching. Secondly, the theory is extended to consider substrates that are not perfectly wetted but exhibit a finite equilibrium contact angle for the coating liquid. This extension incorporates the substrate energetics using a disjoining pressure functional. Unsteady flows are calculated on a substrate of nonuniform wettability. The finite contact angle value required to stop stress-driven flow is predicted and the resulting steady profiles are compared with experimental results for several values of the applied stress.

Suggested Citation

  • Leonard W. Schwartz, 2001. "On the asymptotic analysis of surface-stress-driven thin-layer flow," Springer Books, in: H. K. Kuiken (ed.), Practical Asymptotics, pages 171-188, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0698-9_9
    DOI: 10.1007/978-94-010-0698-9_9
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